Mahendra Singh Dhoni was docked 50 percent of his match fee for breaching IPL's code of conduct during CSK’s encounter with Rajasthan Royals.
Dhoni was penalized for storming onto the field in the final over of Thursday's match as umpiring standards again came into question.
Chennai edged Rajasthan Royals in a last-ball thriller but controversy erupted on the fourth ball of the final over when paceman Ben Stokes bowled a full toss to new batsman Mitchell Santner.
Indian umpire Ulhas Gandhe signalled a no-ball for height, only for his square-leg colleague Bruce Oxenford to overrule that decision and Dhoni, who had been bowled by Stokes on the previous delivery, ran out of the dugout to argue with the officials.
Rajasthan Royals batsman Jos Buttler questioned Dhoni's actions after his team lost the match by four wickets following Santner's six off the final ball.
"I am not sure if that's the right thing to do," Buttler said.
"Obviously tensions are running high in the IPL and every run counts. It was a big moment in the game but whether stepping onto the pitch is quite right, probably not."
Former England captain Michael Vaughan said Dhoni had set a poor example.
"This is not a good look for the game ... No place at all for a Captain to storm onto the pitch from the Dugout ... !! #IPL," he tweeted.
This is not a good look for the game ... No place at all for a Captain to storm onto the pitch from the Dugout ... !! #IPL— Michael Vaughan (@MichaelVaughan) April 11, 2019
Chennai coach Stephen Fleming said Dhoni "just wanted clarity" over the decision but admitted his actions would be "questioned for a long time".
It was the third time umpiring standards have been under the spotlight in this year's IPL, including a no-ball by Lasith Malinga, which was missed by India's Sundaram Ravi that cost Virat Kohli's Royal Challengers Bangalore a win.
"We are not playing club cricket," said Kohli, after Ravi failed to spot a no-ball on the last delivery of the game on March 28.
The controversial 'Mankading' of Buttler by Ravichandran Ashwin also raised questions, as experts said it should have declared a dead ball.